# Literature Review

Albert (1993)

In this paper, Albert uses a Markov switching model to analyze streakiness in baseball pitching data. He concludes that a few players exhibit streakiness, but not enough to reject the null hypothesis. An exploratory technique that we take from this paper is to examine the peaks and valleys in a moving average plot to observe streakiness. A strength of this paper is that Albert controls for situational variables such as home field advantage, the handedness of the pitcher, and the runners on the bases.

Albert (2013)

In this paper, Albert analyzes streakiness in baseball hitting data. His analysis techniques include using Bayes Factors to compare models of the form $$f(y_j|p_j) = p_j(1-p_j)^{y_j}, y_j = 0,1,2,...$$; a consistent model with a constant $$p_j$$, and a streaky model with a varying $$p_j$$ from a beta distribution. A useful insight that we apply to this paper is the concept that the existence of streakiness depends on the definition of “success” in binary outcome data. He found substantially more evidence for streakiness for when a success was coded as “not a strikeout” instead of a “hit”. From this paper, we learn a technique for comparing Bayesian models, and that the organization of the data can affect the outcomes.

Albert & Williamson (1999)

In this paper, Jim Albert attempts to improve upon the low-powered frequentist tests of Gilovich, Vallone, and Tverky’s 1985 paper on the “hot hand”. Albert formally defines “streakiness” as the presence of nonstationarity (nonconstant probability between trials) or autocorrelation (sequential dependency). He uses Gibbs sampling to approximate posterior densities and to simulate data, then fits two types of models on binary data from baseball and basketball to try to characterize streakiness. He fits an overdispersion model to detect nonstationarity, and a Markov switching model to detect sequential dependencies. While he did not uncover strong evidence for the hot hand, one of his takeaways was that overdispersion decreases as time goes on in basketball free throw shooting data. A weakness of this paper is that Albert does not show the results of both the Markov model and the overdispersion model on the same data. We use Albert’s formal definitions of streakiness as well as his motivation for fitting Bayesian models over running frequentist tests.

Ameen & Harrison (1984)

This journal article contains information about discounted likelihood regression using exponential weights, which generalizes to discount weighted estimation (DWE). There is also a section that elaborates on how these models apply to time series. Although the material in this writing focuses on data with a Normal response instead of a Binomial, we use the concepts in this article to help explain our discounted likelihood models in Section 2.1.3.

Bar-Eli et al. (2006)

This paper is a review of previous hot hand research. It reviews several papers investigating the concept of the hot hand in sports such as basketball, baseball, volleyball, and horseshoe, and other fields such as cognitive science and economics. Bar-Eli, Avugos, and Raab evaluate the datasets, the tests and statistics used, and the conclusions of each study. Overall, the authors summarize 13 papers that oppose the hot hand phenomenon, and 11 that support it; they also acknowledge that the scientific evidence for the hot hand is weaker than the evidence against it, and it is typically more controversial. Instead of just looking to answer whether the hot hand exists, Bar-Eli, Avugos, and Raab also examine how people define a “hot hand”, and the psychological factors behind the belief in it, such as the gambling and game strategy. The strengths of this paper are that it evaluates the strengths and weaknesses of many competing claims, and concisely summarizes the information into a table. A weakness is that they do not make any claim of their own. This paper is useful in this thesis because it describes several data analysis techniques to detect streaks in a binary sequence.

Gilovich et al. (1985)

In this research paper from Cognitive Psychology, Thomas Gilovich, Robert Vallone, and Amos Tversky investigate peoples’ belief in the hot hand in basketball. The hot hand is the concept that the probability of a success increases for trials that follow a success in a binary sequence; in basketball, these binary events are shot attempts. The methods in this paper include an analysis of in-game shot attempts from the Philadelphia 76ers of the National Basketball Association (NBA) in the 1981 season, analysis of free-throw attempts from the Boston Celtics in the 1981 and 1982 seasons, and a controlled shooting drill using male and female varsity basketball players at Cornell University. Statistical techniques they used to attempt to detect streakiness in the data included Walf-Wolfowitz run tests, autocorrelation tests on consecutive shot attempts, goodness-of-fit tests for the distribution of successes, and paired t-tests comparing the mean of makes following a make to that of makes following a miss. In addition to this analysis of shooting, this research also contained a survey of basketball fans, that gauged how much people believed success probabilities changed following a success or a failure. The statistical tests did not detect significant evidence supporting the Hot Hand in basketball. The lack of statistical power in Gilovich, Vallone, and Tversky’s frequentist tests motivates the use of Bayesian models in this thesis. Strengths of this paper include the fact that it was one of the first research papers to analyze streakiness in basketball data, and many future papers build off of it. Some weaknesses in this paper are the assumptions it makes in its analysis, such as all shots being independent of each other, and not accounting for shot location.

Joseph (n.d.)

This web page provided a sample of code describing how to implement the “ones trick” in JAGS. The source is from the Lawrence Joseph, a professor in the Department of Epidemiology and Biostatistics of McGill University in Montreal, Quebec. The information from this source was used in the code where we build the model, and in the descriptions of the discounted likelihood hierarchical model in Section 3.1.3.